Double weakness

S. Garti; S. Shelah

doi:10.1007/s10474-021-01132-y

Double weakness

S. Garti^*, S. Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We prove that, consistently, there exists a weakly but not strongly inaccessible cardinal λ for which the sequence ⟨ 2 ^θ: θ< λ⟩ is not eventually constant and the weak diamond fails at λ.We also prove that consistently diamond fails but a parametrized version of weak diamond holds at some strongly inaccessible λ.

Original language	English
Pages (from-to)	379-391
Number of pages	13
Journal	Acta Mathematica Hungarica
Volume	163
Issue number	2
DOIs	https://doi.org/10.1007/s10474-021-01132-y
State	Published - Apr 2021

Bibliographical note

Publisher Copyright:
© 2021, Akadémiai Kiadó, Budapest, Hungary.

Keywords

Cohen forcing
Radin forcing
very weak diamond
weak diamond
weakly inaccessible

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10.1007/s10474-021-01132-y

Cite this

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AU - Shelah, S.

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AB - We prove that, consistently, there exists a weakly but not strongly inaccessible cardinal λ for which the sequence ⟨ 2 θ: θ< λ⟩ is not eventually constant and the weak diamond fails at λ.We also prove that consistently diamond fails but a parametrized version of weak diamond holds at some strongly inaccessible λ.

KW - Cohen forcing

KW - Radin forcing

KW - very weak diamond

KW - weak diamond

KW - weakly inaccessible

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IS - 2

ER -

Double weakness

Abstract

Bibliographical note

Keywords

Access to Document

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